Preheat oven to 425˚F.
Heat 3 tablespoons olive oil in a large dutch-oven skillet or a high-sided oven-proof skillet or pot.
Season lamb shanks with salt and pepper and add to hot oil. Make sure oil is hot because you want that immediate sear on the lamb shanks.
Sear the shanks on all sides until browned.
Remove lamb shanks from skillet and set aside.
Set skillet back over medium-high heat and add in remaining oil.
Add onions, carrots, celery sticks, mushrooms and garlic to the skillet; cook for 4 minutes, stirring frequently.
Slowly pour in chicken broth and stir in wine; stir to loosen all the browned bits on the bottom of the skillet. Bring to a boil.
Place lamb shanks back inside the pot. Add in the fresh herbs.
Put pot in the preheated oven and cook for 1.5 to 2 hours, turning shanks over every 30 to 40 minutes, until meat is tender and internal temperature registers between 150˚F and 160˚F.
Remove pot from oven.
Remove the shanks from the pot; set aside and keep covered.
Simmer remaining sauce that’s in the skillet over medium heat until thickened to a desired consistency, about 6 to 10 minutes.
Skim off any additional fat that rises to the surface.
Taste sauce for seasonings and adjust accordingly.
Add lamb shanks back into the pot.
Garnish with fresh parsley and serve over mashed potatoes, mashed cauliflower, polenta, or rice.